Sub-Areolar Vs Circumareolar Vs SemiAreolar Mastopexy

I understand your confusion and it occurs because these terms are often used improperly.
I have tried to clarify these terms for you:
Sub-Areolar = Dermal Mastopexy
This incision goes all the way around the border of the areola and is essentially a modified circumareolar mastopexy popularized by Dr. Becker. I have tried this with moderate success.
Circum-Areolar=Donut = Benelli=Round Block Masotpexy
This incision goes all the way around the areola. Its benefits are the limited scar. The disadvantage are the inability to predict or prevent the pursestring appearance. It tends to flatten the breast and is best performed with an implant. Various techniques have beed described without an implant and have met with mixed success. Attempts at reducing spreading of the scar necessitate the use of a permanent suture which can have problems with infection, palpability, visibility or nipple puffiness. Many modifications have been described. It cannot be used for advanced ptosis (sagging) which is still better managed with a vertical scar ("lollipop or tennis racket")
Semi-Areolar = Peri-Areolar = Crescent Mastopexy
Good for very minor degrees of sagging. It's benefits are its limited scar. The disadvantage is that it will occasionally stretch or enlarge the areola. I have used it primarily as a method to correct uneven nipple height from one side to the other. I rarely use it for a lift on both sides.
I have prepared a video which amy help to explain the confusion. It is based on a lecture I have given in the past. It has been converted from powerpoint, you may want to enlarge the video to see the pictures more clearly.
I hope this helps.

I think it would be very difficult for anyone to make an informed decision about which type of breast lift to have without the advice of a Board Certified Plastic Surgeon. I would recommend one or more consults by well-trained surgeons in your area who will give you their best advice and recommendations after a thorough discussion and evaluation. This will be, in my opinion, the best way for you to make an informed decision.

The most important thing is not to skimp on the incision for fear of the scar. Why have a shorter scar, but a misshapen breast. If the nipple-areolar complex needs to be moved, then it is best to do a full peri-areolar or circum-areolar incision with a vertical and, most likely, a transverse incision as well. Good luck with your surgery.